We are experiencing a septic drainage situation. Apparently our drainage line is at a "too steep" of an incline and the drainage rushes to the end which doesn't allow proper absorption into the ground. My husband wants to extend the current line using a type of pipe with styrofoam and netting which doesn't require the use of gravel.

My questions are: What is the correct name for this type of pipe? How can I go about looking for some for our little job? Is this method cost-effective? Is this something you would recommend?

"What is the correct name for this type of pipe? How can I go about looking for some for our little job?"
I believe you're thinking of a "Infiltration Leach System" Check them out at;
http://www.thenaturalhome.com/septic.html
Just scroll down to the left hand picture (Infiltrator Leach Field) and click on it.
Never having installed one of these systems I can't comment on how cost effective it will be.
Regards, Tom